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By using first-principles plane-wave ultrasoft pseudopotential method based on the density functional theory, the maximally localized Wannier functions of N vacancy and Al vacancy with different charge states in wurtzite AlN are calculated. With the shape and center of the computed Wannier function, the electronic structure and the spontaneous polarization of vacancy are studied respectively. The results show that N–Al bond possesses a large ionicity. It is found that the electrons of the dangling bonds displace to the positions of vacancies in N vacancy structure, while in Al vacancy structure the electrons of dangling bonds keep away from vacancies and move to the other side of N atoms. Since the vacancy breaks the centrosymmetry of the [1010] and [1210] orientations, the polarization will be induced in these two directions, and the polarization will increase as the charge increases. In the [0001] orientation, the spontaneous polarization in N vacancy will reverse as charge increases because of the dramatic variation of the electronic structure. Contrary to N vacancy, the reversion does not occur although the spontaneous polarization of Al vacancy increases as charge increases.
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Keywords:
- vacancy /
- maximally localized Wannier functions /
- spontaneous polarization /
- first-principles
[1] Taniyasu Y, Kasu M, Makimoto T 2006 Nature 441 325
[2] Nishida T, Saito H, Kobayashi N 2001 Appl. Phys. Lett. 79 711
[3] Walker D, Zhang X, Kung P, Saxler A, Javadpour S, Xu J, Razeghi M 1996 Appl. Phys. Lett. 68 2100
[4] Hung A, Russo S P, McCulloch D G, Prawer S 2004 J. Chem. Phys. 120 4890
[5] Zhong W, King-Smith R D, Vanderbilt D 1994 Phys. Rev. Lett. 72 3618
[6] Bernardini F, Fiorentini V, Vanderbilt D 1997 Phys. Rev. B 56 10024
[7] Maki J M, Makkonen I, Tuomisto F, Karjalainen A, Suihkonen S, Raisanen J, Chemekova T Y, Makarov Y N 2011 Phys. Rev. B 84 081204
[8] Schulz T, Albrecht M, Irmscher K, Hartmann C, Wollweber J, Fornari R 2011 Phys. Status Solidi B 248 1513
[9] Kingsmith R D, Vanderbilt D 1993 Phys. Rev. B 47 1651
[10] Marzari N, Vanderbilt D 1997 Phys. Rev. B 56 12847
[11] Benson D, Sankey O F, Häussermann U 2011 Phys. Rev. B 84 125211
[12] Gao F, Bylaska E J, El-Azab A, Weber W J 2004 Appl. Phys. Lett. 85 5565
[13] Corsetti F, Mostofi A A 2011 Phys. Rev. B 84 035209
[14] Gao S P, Zhu T 2012 Acta Phys. Sin. 61 137103 (in Chinese) [高尚鹏, 祝桐 2012 物理学报 61 137103]
[15] Marzari N, Mostofi A A, Yates J R, Souza I, Vanderbilt D 2012 Rev. Mod. Phys. 84 1419
[16] Andrinopoulos L, Hine N D, Mostofi A A 2011 J. Chem. Phys. 135 154105
[17] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Smogunov A, Umari P, Wentzcovitch R M 2009 J. Phys.: Condens. Matter 21 395502
[18] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[19] Ye H G, Chen G D, Zhu Y Z, Zhang J W 2007 Acta Phys. Sin. 56 5376 (in Chinese) [耶红刚, 陈光德, 竹有章, 张俊武 2007 物理学报 56 5376]
[20] Abu-Farsakh H, Qteish A 2007 Phys. Rev. B 75 085201
[21] Lahnemann J, Brandt O, Jahn U, Pfuller C, Roder C, Dogan P, Grosse F, Belabbes A, Bechstedt F, Trampert A, Geelhaar L 2012 Phys. Rev. B 86 081302
[22] Ye H G, Chen G D, Zhu Y Z, Lu H M 2007 Chin. Phys. 16 3803
[23] Yates J R, Wang X J, Vanderbilt D, Souza I 2007 Phys. Rev. B 75 195121
[24] Laaksonen K, Ganchenkova M G, Nieminen R M 2009 J. Phys.: Condens. Matter 21 015803
[25] Vail J M, Schindel D, Yang A, Penner O, Pandey R, Jiang H, Blanco M A, Costales A, Qiu Q C, Xu Y 2004 J. Phys.: Condens. Matter 16 3371
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[1] Taniyasu Y, Kasu M, Makimoto T 2006 Nature 441 325
[2] Nishida T, Saito H, Kobayashi N 2001 Appl. Phys. Lett. 79 711
[3] Walker D, Zhang X, Kung P, Saxler A, Javadpour S, Xu J, Razeghi M 1996 Appl. Phys. Lett. 68 2100
[4] Hung A, Russo S P, McCulloch D G, Prawer S 2004 J. Chem. Phys. 120 4890
[5] Zhong W, King-Smith R D, Vanderbilt D 1994 Phys. Rev. Lett. 72 3618
[6] Bernardini F, Fiorentini V, Vanderbilt D 1997 Phys. Rev. B 56 10024
[7] Maki J M, Makkonen I, Tuomisto F, Karjalainen A, Suihkonen S, Raisanen J, Chemekova T Y, Makarov Y N 2011 Phys. Rev. B 84 081204
[8] Schulz T, Albrecht M, Irmscher K, Hartmann C, Wollweber J, Fornari R 2011 Phys. Status Solidi B 248 1513
[9] Kingsmith R D, Vanderbilt D 1993 Phys. Rev. B 47 1651
[10] Marzari N, Vanderbilt D 1997 Phys. Rev. B 56 12847
[11] Benson D, Sankey O F, Häussermann U 2011 Phys. Rev. B 84 125211
[12] Gao F, Bylaska E J, El-Azab A, Weber W J 2004 Appl. Phys. Lett. 85 5565
[13] Corsetti F, Mostofi A A 2011 Phys. Rev. B 84 035209
[14] Gao S P, Zhu T 2012 Acta Phys. Sin. 61 137103 (in Chinese) [高尚鹏, 祝桐 2012 物理学报 61 137103]
[15] Marzari N, Mostofi A A, Yates J R, Souza I, Vanderbilt D 2012 Rev. Mod. Phys. 84 1419
[16] Andrinopoulos L, Hine N D, Mostofi A A 2011 J. Chem. Phys. 135 154105
[17] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Smogunov A, Umari P, Wentzcovitch R M 2009 J. Phys.: Condens. Matter 21 395502
[18] Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[19] Ye H G, Chen G D, Zhu Y Z, Zhang J W 2007 Acta Phys. Sin. 56 5376 (in Chinese) [耶红刚, 陈光德, 竹有章, 张俊武 2007 物理学报 56 5376]
[20] Abu-Farsakh H, Qteish A 2007 Phys. Rev. B 75 085201
[21] Lahnemann J, Brandt O, Jahn U, Pfuller C, Roder C, Dogan P, Grosse F, Belabbes A, Bechstedt F, Trampert A, Geelhaar L 2012 Phys. Rev. B 86 081302
[22] Ye H G, Chen G D, Zhu Y Z, Lu H M 2007 Chin. Phys. 16 3803
[23] Yates J R, Wang X J, Vanderbilt D, Souza I 2007 Phys. Rev. B 75 195121
[24] Laaksonen K, Ganchenkova M G, Nieminen R M 2009 J. Phys.: Condens. Matter 21 015803
[25] Vail J M, Schindel D, Yang A, Penner O, Pandey R, Jiang H, Blanco M A, Costales A, Qiu Q C, Xu Y 2004 J. Phys.: Condens. Matter 16 3371
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